details

property	value
status	complete
benchmark	size-12-alpha-3-num-439.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n128.star.cs.uiowa.edu
space	Waldmann_07_size12

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	9.11945 seconds
cpu usage	26.8188
user time	25.7977
system time	1.02109
max virtual memory	4.1494776E7
max residence set size	2934516.0

stage attributes

key	value
starexec-result	YES

output

22.82/6.81 YES 25.85/7.85 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 25.85/7.85 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 25.85/7.85 25.85/7.85 25.85/7.85 Termination w.r.t. Q of the given QTRS could be proven: 25.85/7.85 25.85/7.85 (0) QTRS 25.85/7.85 (1) DependencyPairsProof [EQUIVALENT, 21 ms] 25.85/7.85 (2) QDP 25.85/7.85 (3) QDPOrderProof [EQUIVALENT, 154 ms] 25.85/7.85 (4) QDP 25.85/7.85 (5) UsableRulesProof [EQUIVALENT, 0 ms] 25.85/7.85 (6) QDP 25.85/7.85 (7) QDPSizeChangeProof [EQUIVALENT, 0 ms] 25.85/7.85 (8) YES 25.85/7.85 25.85/7.85 25.85/7.85 ---------------------------------------- 25.85/7.85 25.85/7.85 (0) 25.85/7.85 Obligation: 25.85/7.85 Q restricted rewrite system: 25.85/7.85 The TRS R consists of the following rules: 25.85/7.85 25.85/7.85 a(x1) -> b(c(x1)) 25.85/7.85 a(a(x1)) -> x1 25.85/7.85 a(b(b(x1))) -> b(b(a(a(x1)))) 25.85/7.85 25.85/7.85 Q is empty. 25.85/7.85 25.85/7.85 ---------------------------------------- 25.85/7.85 25.85/7.85 (1) DependencyPairsProof (EQUIVALENT) 25.85/7.85 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 25.85/7.85 ---------------------------------------- 25.85/7.85 25.85/7.85 (2) 25.85/7.85 Obligation: 25.85/7.85 Q DP problem: 25.85/7.85 The TRS P consists of the following rules: 25.85/7.85 25.85/7.85 A(b(b(x1))) -> A(a(x1)) 25.85/7.85 A(b(b(x1))) -> A(x1) 25.85/7.85 25.85/7.85 The TRS R consists of the following rules: 25.85/7.85 25.85/7.85 a(x1) -> b(c(x1)) 25.85/7.85 a(a(x1)) -> x1 25.85/7.85 a(b(b(x1))) -> b(b(a(a(x1)))) 25.85/7.85 25.85/7.85 Q is empty. 25.85/7.85 We have to consider all minimal (P,Q,R)-chains. 25.85/7.85 ---------------------------------------- 25.85/7.85 25.85/7.85 (3) QDPOrderProof (EQUIVALENT) 25.85/7.85 We use the reduction pair processor [LPAR04,JAR06]. 25.85/7.85 25.85/7.85 25.85/7.85 The following pairs can be oriented strictly and are deleted. 25.85/7.85 25.85/7.85 A(b(b(x1))) -> A(a(x1)) 25.85/7.85 The remaining pairs can at least be oriented weakly. 25.85/7.85 Used ordering: Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]: 25.85/7.85 25.85/7.85 <<< 25.85/7.85 POL(A(x_1)) = [[0A]] + [[0A, -I, -I]] * x_1 25.85/7.85 >>> 25.85/7.85 25.85/7.85 <<< 25.85/7.85 POL(b(x_1)) = [[0A], [0A], [0A]] + [[0A, 1A, -I], [-I, 0A, 0A], [0A, 1A, 0A]] * x_1 25.85/7.85 >>> 25.85/7.85 25.85/7.85 <<< 25.85/7.85 POL(a(x_1)) = [[0A], [0A], [0A]] + [[-I, 0A, 0A], [0A, -I, -I], [0A, -I, -I]] * x_1 25.85/7.85 >>> 25.85/7.85 25.85/7.85 <<< 25.85/7.85 POL(c(x_1)) = [[0A], [-I], [0A]] + [[-I, -I, -I], [-I, -I, -I], [0A, -I, -I]] * x_1 25.85/7.85 >>> 25.85/7.85 25.85/7.85 25.85/7.85 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 25.85/7.85 25.85/7.85 a(x1) -> b(c(x1)) 25.85/7.85 a(a(x1)) -> x1 25.85/7.85 a(b(b(x1))) -> b(b(a(a(x1)))) 25.85/7.85 25.85/7.85 25.85/7.85 ---------------------------------------- 25.85/7.85 25.85/7.85 (4) 25.85/7.85 Obligation: 25.85/7.85 Q DP problem: 25.85/7.85 The TRS P consists of the following rules: 25.85/7.85 25.85/7.85 A(b(b(x1))) -> A(x1) 25.85/7.85 25.85/7.85 The TRS R consists of the following rules: 25.85/7.85 popout

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